Tropical Noether formula

Let $X$ be a compact tropical surface. Its topological Euler characteristic is denoted by $\chi(X)$, and let $K_X^2$ and $c_2(X)$ denote the square of its canonical class and its top tropical Chern class, respectively.

Tropical Noether formula.

$$\chi(X)=\frac{K_X^2+c_2(X)}{12}.$$

This is the tropical analogue of Noether's formula for classical projective surfaces, replacing the holomorphic Euler characteristic by the topological Euler characteristic. The source does not state a resolution of the formula.